Answer
$ 6.5\%$ compounded semiannually yields about $\$ 221$ more than $6 \%$ compounded continuously.
Work Step by Step
The formula for compounded interest with $ n $ compounding semiannually $ 6.5\%$ is given by : $ A= P(1+\dfrac{r}{n} )^{nt}$
Plug in the given data.
$ A= 3000 (1+\dfrac{0.065}{2} )^{ 2 \cdot 10} \approx \$ 5,687.51$
Now, the formula for continuously compounded interest $6 \%$ is given by : $ A= Pe^{rt}$
Plug in the given data.
$ A= 3,000 \times e^{0.06 \cdot 10} \approx \$ 5,466.36$
We can see that $ 6.5\%$ compounded semiannually yields about $\$ 221$ more than $6 \%$ compounded continuously.
